A Two‐Dimensional Transformed Differential Quadrature Solution for Air‐Hydro‐Mechanical Coupling in Layered Unsaturated Soils

ABSTRACT Layered unsaturated soils are a prevalent form of shallow soils, and their consolidation process is pretty complex due to the interaction of three phases, including solid, water, and air. In practical ground improvement projects, sand drain techniques are commonly employed to accelerate the consolidation rate in the horizontal direction. Therefore, the consolidation process cannot be simplified as a one‐dimensional problem. This study established a two‐dimensional consolidation analysis system for layered unsaturated soil media, considering the flow of both pore water and pore air, as well as the continuity conditions between unsaturated soil layers. Subsequently, the static equilibrium equations and the constitutive equations for unsaturated soils are incorporated into the system to obtain the deformation distribution at any point within the unsaturated soil media over time. A novel solution to this system is derived based on the transformed differential quadrature method by combining the Laplace integral transform technique and differential quadrature rules, where the former is employed to address the time‐dependent partial differential terms, and the latter is utilized to discretize the spatial domain. The inverse Laplace transform is then conducted to obtain the solution in the physical domain. The proposed solution is validated by comparing the results with existing analytical solutions. Furthermore, the effects of permeability coefficients, mechanical properties of the unsaturated soil interlayer, and the horizontal spacing of sand drains on the two‐dimensional consolidation behavior of layered unsaturated soil media are analyzed.